Projection domain decomposition has been used to reduce beam hardening distortions present in low and high energy (spectrum) images of dual-energy CT. Unfortunately, projection domain decomposition introduces strong negatively correlated noise between Compton scatter and photoelectric effect line integrals. A de-noising algorithm can be used to reduce the noise. However, reducing the low-frequency component of the noise with such a de-noising algorithm without smearing the image or introducing some bias can be challenging. Independent of this challenge, the non-linear projection domain decomposition of noisy input projection data leads, by itself, to noise induced bias. Part of this bias remains in-spite of applying a de-noising algorithm, propagates to the image, and can degrade the spectral image quality.